相关论文: Gluing and Hilbert functions of monomial curves
We describe the cone of Hilbert functions of artinian graded modules finitely generated in degree 0 over the polynomial ring R = k[x, y] with the non-standard grading deg(x) = 1 and deg(y) = n, where n is any natural number.
In this note, we study commutative Noetherian local rings having finitely generated modules of finite Gorenstein injective dimension. In particular, we consider whether such rings are Cohen-Macaulay.
We extend the group theoretic construction of local models of Pappas and Zhu to the case of groups obtained by Weil restriction along a possibly wildly ramified extension. This completes the construction of local models for all reductive…
Let $C$ be a nodal curve, and let $E$ be a union of semistable subcurves of $C$. We consider the problem of contracting the connected components of $E$ to singularities in a way that preserves the genus of $C$ and makes sense in families,…
We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff…
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…
Pilgrim's Finite Global Attractor Conjecture has been verified for polynomials [1], but remains open for general rational maps. In this paper, we prove the conjecture for a family of rational maps obtained by gluing two PCF polynomials…
The Jordan type of an Artinian algebra is the Jordan block partition associated to multiplication by a generic element of the maximal ideal. We study the Jordan type for Artinian Gorenstein (AG) local algebras A, and the interaction of…
We generalise notions of Gorenstein homological algebra for rings to the context of arbitrary abelian categories. The results are strongest for module categories of rngs with enough idempotents. We also reformulate the notion of Frobenius…
Given two semigroups $\langle A\rangle$ and $\langle B\rangle$ in ${\mathbb N}^n$, we wonder when they can be glued, i.e., when there exists a semigroup $\langle C\rangle$ in ${\mathbb N}^n$ such that the defining ideals of the…
A new construction of rings is introduced, studied, and applied. Given surjective homomorphisms $R\to T\gets S$ of local rings, and ideals in $R$ and $S$ that are isomorphic to some $T$-module $V$, the \emph{connected sum} $R#_TS$ is…
We adapt "Obstruction Bundle Gluing (OBG)" techniques from Hutchings and Taubes (arxiv: 0701300, 0705.2074) to Morse theory. We consider Morse function-metric pairs with gradient flowlines that have nontrivial yet well-controlled cokernels…
We show that two smooth nearby Riemannian metrics can be glued interpolating their scalar curvature. The resulting smooth metric is the same as the starting ones outside the gluing region and has scalar curvature interpolating between the…
We show that the gluing construction for Hilbert modules introduced by Raeburn in his computation of the Picard group of a continuous-trace C*-algebra (Trans. Amer. Math. Soc., 1981) can be applied to arbitrary C*-algebras, via an algebraic…
The purpose of this short note is to study Serre functors of categories of quasicoherent sheaves on stacks of the form $\mathcal{Y} = \mathrm{Spec} A/G$ where $G$ is a reductive group acting on $\mathrm{Spec} A$ with a unique closed orbit.…
A commutative ring $R$ is stable provided every ideal of $R$ containing a nonzerodivisor is projective as a module over its ring of endomorphisms. The class of stable rings includes the one-dimensional local Cohen-Macaulay rings of…
This paper considers the following conjecture: If $R$ is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal $J$ generated by a system of parameters, the Chern coefficient…
Ara\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups. We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest…
We reinterpret various properties of Noetherian local rings via the existence of some $n$-ary numerical function satisfying certain uniform bounds. We provide such characterizations for seminormality, weak normality, generalized…
We determine the adjoint trace field of gluings of general hyperbolic manifolds. This provides a new method to prove the nonarithmeticity of gluings, which can be applied to the classical construction of Gromov and Piatetski-Shapiro (and…